The development of a fertilized egg to an embryo requires the proper temporal control of gene expression. During cell differentiation, timing is often controlled via cascades of transcription factors (TFs). However, in early development, transcription is often inactive, and many TF levels stay constant, suggesting that alternative mechanisms govern the observed rapid and ordered onset of gene expression. Here, we find that in early embryonic development access of maternally deposited nuclear proteins to the genome is temporally ordered via importin affinities, thereby timing the expression of downstream targets. We quantify changes in the nuclear proteome during early development and find that nuclear proteins, such as TFs and RNA polymerases, enter the nucleus sequentially. Moreover, we find that the timing of nuclear proteins' access to the genome corresponds to the timing of downstream gene activation. We show that the affinity of proteins to importin is a major determinant in the timing of protein entry into embryonic nuclei. Thus, we propose a mechanism by which embryos encode the timing of gene expression in early development via biochemical affinities. This process could be critical for embryos to organize themselves before deploying the regulatory cascades that control cell identities.